Discussion Forum

write 2 coupled equations for real and imaginary part of A in pde modes
JF

Dear JF,

Thank you for your reply.
So, you mean that I need to decompose the PDE into two equations, one of which is real part equation
and the other is imaginary part equation?

Could you give me some references or comsol example files on this subject if you happen to have ?

Thank you very much.

Yoon

Hi

I'm not often using Comsol in that way, but its interesting to try so here re my comments live, how I would start, we will then see how far we come, pls check carefully as I might do stupid errors too ;)

1) as you have not defined the dimensions of "A" the dependent variable I'll start with 1D, you can always apply in 2D 2Daxi or 3D by analogy, do not forget that by default COMSOL is in cartesian representation and that you must apply coordinate transforms to be in spherical see the knowledge base on detals on coordinate transforms

2) the "jwA" tells me that we are in harmonic or eigenfrequency mode and then its to decide if we are to use the coefficient or General form of the PDE Modes, I'll use coefficient form to start with, even if COMSOL transforms it into general form internally

3) I'll use 3.5 and not 4, as the equations are better shown (for the moment, equations has been promished for futur updates of V4)

so =>
a) CM3.5 + New + 1D + PDE, Coefficient form + Eigenvalue analysis, + A as dependent variable + OK,
b) define C as a Constant "C"=1 to start with (upper case it's the one in your equation to distinguish from the COMSOL internal "c"
c) draw a line from "0" to "1" for the geometry
d) ignore materials
e) in subdomain Settings use c=1 alpha=gamma=0 a=C beta=0 f=0 ea=0 da=1, note lambda = j*w (for me but here I'm not sure, not explicitly written out in the doc)
f) you need to define the boundary conditions, by default Dirichlet at the two vertexes = 0
g) Solve

You get a nice first mode curve, in Postprocessing Plot Parameters you can change the different eigenvalue modes

In PDE General form I would use:
Gamma = -Ax , F = -C*A , ea=0 , da=1

Note in V4 the default boundary conditions are no flux Neumann, while in V3.5 it's Dirichlet 0 value

It looks certainly nice ;) It's certainly also mathematically correct w.r.t the definitions we put into COMSOL, but does it fit to your demand I do not really know, would have to write out and check by hand, no time just now

note that the spatial solution is A(x)=sqrt(2)*sin(1/pi*x) with temporal eigenmodes at 1+(n*pi)^2 (V3.5 case) sounds familar

Have fun Comsoling
Ivar

Dear Ivar

I appreciate your kind explanation. I will try your method and post results if they are useful.

Yoon